An astronomical telescope has a large aperture to

Three immiscible transparent liquids with uniform refractive indices $\frac{3}{2}, \frac{4}{3}$ and $\frac{6}{5}$ are arranged one on top of another. The depths of the liquids are 3 cm 4 cm and 6 cm respectively. The apparent depth of the vessel is

Velocity of light in diamond is $\left(\frac{5}{12}\right)^{\text {th }}$ times that in air. Velocity of light in water is $\left(\frac{3}{4}\right)^{\text {th }}$ times that in air. The angle of incidence of ray of light travelling from water to diamond is (angle of refraction $\left.(\mathrm{r})=30^{\circ}\right)\left[\right.$ Given $\left.\rightarrow \sin 30^{\circ}=\frac{1}{2}\right]$

A point object kept at P in front of a glass sphere of radius ' $R$ ' has its image formed at $Q$ such that $\mathrm{PO}=\mathrm{QO}$. The refractive index of material of glass sphere is 1.4. The distance PO is equal to